Question

There are two circles , one large and one small. The radius of the large circle is three times the radius of the small circle. Find the value of the of the fraction: area of small circle/ area of large circle

Answer 1

Answer:

radius of small circle =x

radius of large circle=3x

area of small circle=πx^2

area of large circle=9πx^2

area of small circle/area of large circle

πx^2/9πx^2

1/9....answer

Answer 2

Let R be the radius of the large circle and r be that of the small circle.

Given that R = 3r

$∴ \frac{area \: of \: small \: cirle}{area \: of \: large \: circle} = \frac{2\pi {r}^{2} }{2\pi {R}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ {r}^{2} }{ {R}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{r}{3r}$

$= \frac{1}{3}$